Group theory is fun, but in this case I can't get even started, though the puzzle seems trivial. I tried searching ProofWiki's group theory section for something useful, but I couldn't find anything. So, any help is welcome. Thank you.

Group theory is fun, but in this case I can't get even started, though the puzzle seems trivial. I tried searching ProofWiki's group theory section for something useful, but I couldn't find anything. So, any help is welcome. Thank you.

Define $\displaystyle f:C_n\rightarrow \langle c^m\rangle\,,\,\,f(g):=g^m$ ; since the group is abelian this is a homomorphism whose